Some Error Analysis for the Quantum Phase Estimation Algorithms

This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random approximations are used for the unitary operator, e.g., the QDRIFT method \cite{campbell2019random}. We characterize the probability of computing the phase values in terms of the consistency error, including the residual error, Trotter splitting error, or statistical error.